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Prove that the function f(x)=x^3-3x^2+3x...

Prove that the function `f(x)=x^3-3x^2+3x-100` is increasing on `R` .

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RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Find the intervals in which the function f given by f(x)=sinx+cosx ,\...

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  2. Find f ' (x) iff(x)= sin3xcos3x

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  3. Prove that the function f(x)=x^3-3x^2+3x-100 is increasing on R .

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  4. Let I be an interval disjointed from [-1,\ 1] . Prove that the functio...

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  5. Show that the function f(x)=3/x+7 is decreasing for x in R-{0} .

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  6. Show that the function x+1//x is increasing for x >1 .

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  7. Find the second order derivative of function f(x)=sinx+cosx with respe...

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  8. Prove that f(theta)=(4sintheta)/(2+costheta)-theta is an increasing fu...

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  9. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

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  10. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) is increasing on R .

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  11. Test whether the function f(x)=x^3-8 is increasing on [1,\ 2] .

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  12. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

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  13. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

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  14. On which of the following intervals, the function x^(100)+sinx-1 is...

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  15. Determine the values of x for which f(x)=x^x ,\ x >0 is increasing or ...

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  16. Find the intervals in which f(x)=x/(logx) is increasing or decreasing

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  17. If a ,\ b ,\ c are real numbers, then find the intervals in which f(...

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  18. Show that for ageq1,\ \ f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on ...

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  19. Show that f(x)=cos(2x+pi//4) is an increasing function on (3pi//8,\ 7p...

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  20. Find the least value of ' a ' such that the function f(x)=x^2+a x+1 is...

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